Short answer
There is no single worldwide rule. Storage advice reflects whether eggs were washed, how they entered the cold chain and the food-safety system in the country where they were sold.
Washed eggs and the cold chain
Commercial eggs in the US and Canada are washed and sanitised under controlled conditions, then refrigerated. Washing changes the shell’s protective surface, so those eggs should remain cold. Temperature cycling can cause condensation that assists movement of contamination.
UK and European retail practice
Class A eggs are generally not washed and are often sold without refrigeration to avoid major temperature swings. That does not mean a warm kitchen is ideal. UK guidance commonly recommends storing eggs in their box in the refrigerator at home.
The rule to follow
Use the carton and national food authority for the eggs in front of you. Once eggs have been refrigerated, keep them refrigerated. Store them away from strong odours and temperature changes, preferably in the main body of the fridge rather than the door.